School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China.
Phys Rev E. 2018 Jul;98(1-1):012304. doi: 10.1103/PhysRevE.98.012304.
The synchronization behavior of networked chaotic oscillators with periodic coupling is investigated. It is observed in simulations that the network synchronizability could be significantly influenced by tuning the coupling frequency, even making the network alternating between the synchronous and nonsynchronous states. Using the master stability function method, we conduct a detailed analysis of the influence of coupling frequency on network synchronizability and find that the network synchronizability is maximized at some characteristic frequencies comparable to the intrinsic frequency of the local dynamics. Moreover, it is found that as the amplitude of the coupling increases, the characteristic frequencies are gradually decreased. Using the finite-time Lyapunov exponent technique, we investigate further the mechanism for the maximized synchronizability and find that at the characteristic frequencies the power spectrum of the finite-time Lyapunov exponent is abruptly changed from the localized to broad distributions. When this feature is absent or not prominent, the network synchronizability is less influenced by the periodic coupling. Our study shows the efficiency of finite-time Lyapunov exponent in exploring the synchronization behavior of temporally coupled oscillators and sheds lights on the interplay between the system dynamics and structure in general temporal networks.
研究了具有周期耦合的网络混沌振荡器的同步行为。通过模拟观察到，通过调整耦合频率可以显著影响网络同步能力，甚至使网络在同步和不同步状态之间交替。使用主稳定性函数方法，我们对耦合频率对网络同步能力的影响进行了详细分析，发现网络同步能力在某些特征频率处最大化，这些特征频率与局部动力学的固有频率相当。此外，还发现随着耦合幅度的增加，特征频率逐渐降低。使用有限时间李雅普诺夫指数技术，我们进一步研究了最大化同步能力的机制，发现特征频率处的有限时间李雅普诺夫指数的功率谱从局域分布突然变为宽带分布。当不存在或不明显时，网络同步能力受周期耦合的影响较小。我们的研究表明了有限时间李雅普诺夫指数在探索时变耦合振荡器的同步行为方面的有效性，并揭示了系统动力学和一般时变网络结构之间的相互作用。
